How many such pairs of letters are there in the word CORPORATE each of...
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List of positions:
C(1), O(2), R(3), P(4), O(5), R(6), A(7), T(8), E(9)
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Alphabet positions:
C=3, O=15, R=18, P=16, A=1, T=20, E=5
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Check pairs:
- O and P (positions 2 and 4): 1 letter between in word, 1 letter between in alphabet.
- O and R (positions 2 and 6): 3 letters between in word, 3 letters between in alphabet.
- O and T (positions 2 and 8): 5 letters between in word, 5 letters between in alphabet.
Answer: There are three such pairs.
Correct option: c) Three.
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How many such pairs of letters are there in the word CORPORATE each of...
Understanding the Problem
The task is to find pairs of letters in the word "CORPORATE" such that the number of letters between them in the word matches the number of letters between them in the English alphabet.
Steps to Solve
1. Identify the Letters:
The letters in "CORPORATE" are: C, O, R, P, O, R, A, T, E.
2. Check Each Pair:
We'll compare each letter with every other letter that comes after it and see if the distance between them in the word matches the distance in the alphabet.
Pairs of Letters
- C and O:
- In the word: 1 letter (R) between C and O.
- In the alphabet: C(3) to O(15) = 15 - 3 - 1 = 11 (not a match).
- C and R:
- In the word: 2 letters (O, R) between C and R.
- In the alphabet: C(3) to R(18) = 18 - 3 - 1 = 14 (not a match).
- C and A:
- In the word: 5 letters (O, R, P, O, R) between C and A.
- In the alphabet: C(3) to A(1) = 1 + 26 - 3 - 1 = 23 (not a match).
- C and T:
- In the word: 6 letters (O, R, P, O, R, A) between C and T.
- In the alphabet: C(3) to T(20) = 20 - 3 - 1 = 16 (not a match).
- O and R:
- In the word: 0 letters between O and R.
- In the alphabet: O(15) to R(18) = 3 - 1 = 2 (not a match).
- O and A:
- In the word: 5 letters between O and A.
- In the alphabet: O(15) to A(1) = 1 + 26 - 15 - 1 = 11 (not a match).
- R and P:
- In the word: 0 letters between R and P.
- In the alphabet: R(18) to P(16) = 2 - 1 = 1 (not a match).
- A and T:
- In the word: 0 letters between A and T.
- In the alphabet: A(1) to T(20) = 20 - 1 - 1 = 18 (not a match).
Identified Pairs
The pairs that match the criteria are:
1. (C, R): 2 letters between them in the word and 14 in the alphabet.
2. (O, A): 5 letters between them in the word and 11 in the alphabet.
3. (R, E): 2 letters between them in the word and 2 in the alphabet.
Thus, the correct answer is